p(Y|A, L) = N(p(Y|A,L)(A,L), 0.5)

Here, \(\vec{\psi }_{p(W,Z|L)}, \vec{\psi }_{p(A|L)}, \vec{\mu }_{p(Y|A,L)}\)  are neural networks. We provide the structure of neural nets in Table REF  and REF . Following the orignal work [1]}, we train all neural nets by Adamax [2]} with a learning rate of 0.01, which was annealed with an exponential decay schedule. We also performed early stopping according to the lower bound on a validation set. To predict structural function, we obtain \(q(L)\)  by marginalizing \(q(L|A,Z,W,Y)\)  by observed data \(A,Z,W,Y\) . We then output \(\hat{f}_{\mathrm {struct}}(a) = [L\sim q(L)]{[Y\sim p(Y|A=a,L)]{Y}}\) .
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